We are interested in estimating the intractable posterior distribution of unobserved variable \(y\)  given an observation \(x\) . One particular class of neural density estimators that scales well to high-dimensional data is normalizing flows (NFs) [1]} - the technique that was applied to inverse problems in various domains, including astronomy [2]}, lattice field theory [3]}, and high energy physics [4]}. In the framework, a latent random variable \(u\)  distributed according to a simple base distribution \(p(u)\)  undergoes a sequence of \(K\)  invertible parameterized transformations \(z_k = f_k(z_{k-1})\) , where \(z_0 = u\)  and \(z_K = x\) . The framework can be further generalized to model the posterior distribution \(p(x|y)\)  by conditioning each function \(f_k\)  as well as the prior distribution \(p_\theta (u|y)\)  to the context variable \(y\) . For a model density \(p_K(x|y)\)  to approximate the true density \(p(x|y)\) , the negative log-likelihood of the observed data under the model is minimized.
